Details

sample72.0ms

Algorithm

intervals

Results

25.0ms	45×	body	2560	valid
15.0ms	48×	body	1280	valid
9.0ms	48×	body	640	valid
4.0ms	29×	body	320	valid
4.0ms	15×	body	160	valid
3.0ms	71×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize27.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
12.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

7.0ms	(- 1.0 (cos x))
22.0ms	(/ (- 1.0 (cos x)) (* x x))

series499.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1.0 (cos x))
478.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify599.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (170.0ms)

Iter	Nodes	Cost
0	88	507
1	232	489
2	1094	441
done	5001	441

prune184.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

26.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series133.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (/ (- 1.0 (cos x)) x) x)
57.0ms	(/ (- 1.0 (cos x)) x)
24.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

156 → 156

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	229	2262
1	549	2156
2	2484	2048
done	5000	2028

prune478.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

99.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
7.0ms	(pow (cos x) 3)
13.0ms	(+ 1.0 (cos x))
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series342.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
50.0ms	(pow (cos x) 3)
18.0ms	(+ 1.0 (cos x))
77.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.0s

Counts

201 → 201

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	260	5407
1	684	5088
2	2983	4980
done	5001	4978

prune694.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
0.9b	(log (exp (pow (cos x) 3)))
1.8b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

6.0ms	(pow (cos x) 3)
6.0ms	(+ 1.0 (cos x))
8.0ms	(log (exp (pow (cos x) 3)))
52.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (cos x) 3)
22.0ms	(+ 1.0 (cos x))
48.0ms	(log (exp (pow (cos x) 3)))
67.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify892.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	140	922
1	357	707
2	1488	660
done	5000	660

prune273.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

regimes62.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch152.0ms

Steps

Iters	Range		Point
9	0.00015484893005477947	28918.939680702064	0.03382760307135756
10	-2676750800.736259	-2.9526231381329305e-09	-0.03237572141906872

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	93
1	60	93
done	60	93

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	1568×	body	2560	valid
665.0ms	1295×	body	1280	valid
345.0ms	1433×	body	640	valid
208.0ms	944×	body	320	valid
122.0ms	2324×	body	80	valid
51.0ms	436×	body	160	valid